1. Field of the Invention
The present invention relates to a method for analyzing a membrane structure and an apparatus therefor. More particularly, the invention relates to a method for analyzing a membrane structure by simultaneously fitting simulated operation data to measured data obtained with an optical system utilizing at least two sets of resolutions and dynamic ranges, and an apparatus therefor.
2. Description of the Related Art
In the X-ray reflectivity measurement, an interference phenomenon of X-rays reflected on interfaces among layers of a membrane is measured, and simulated operation data is fitted to the measurement results to analyze density, membrane thickness and roughness of the respective layers. The density of the outermost thin layer can be calculated from the total reflection critical angle, and the densities of the other layers can be calculated from the amplitudes of the interference fringes. The membrane thickness of the layers can be calculated from the frequencies of vibrations. The roughness can be calculated from the attenuation ratio of the total reflectivity measurement data and the attenuation of the amplitudes of the interference fringes on the higher angle side (as described for example in JP-A-2001-349849).
In the case where the X-ray reflectivity measurement is applied to a multi-layer thin membrane having a layer thickness of several hundred nanometers, it is necessary that the measurement is carried out with the divergence angle and the wavelength spread of the incident X-ray being set to sufficiently small values. For example, a perfect crystal monochromator of Si or Ge is used on the incident side. The perfect crystal monochromator suppresses the wavelength of the X-ray generated by a light source from being spread and abstracts only the parallel component from the X-ray, and therefore, the intensity of the X-ray thus irradiating the thin membrane is reduced by about from 1/10 to 1/100 in comparison to the case using no perfect crystal monochromator. In the case where a four-crystal optical system is used, in particular, the intensity of the incident X-ray is reduced to about 1/100, and there are some cases where a sufficient dynamic range cannot be obtained upon X-ray reflectivity measurement.
That is, in the case where the perfect crystal monochromator is used, the measurement cannot be attained to the higher angle side due to the small dynamic range, and there are some cases where the roughness cannot be sufficiently evaluated. In the case where a thin layer is present in the multi-layer membrane, furthermore, there are some cases where the fitting goes with neglecting the layer since the period of vibration corresponding to the layer thickness is small.
FIG. 3 shows a profile as a result of analysis of measurement data of an Si thin membrane with an optical system using a Ge(220) four-crystal monochromator (divergence angle of incident X-ray: about 0.0045°). As a result of fitting of simulated data to the measured data, it is expected that the thin membrane is a single layer membrane formed on a substrate, and in the analysis results shown in Table 2 below, the R value is 0.01586, which shows good agreement.
TABLE 2DensityThicknessRoughness(g/cm3)(nm)(nm)R valueSi2O3CH31.012398.301.450.01586Si substrate2.33—0.81
However, in the case where the fitting is again carried out with different initial values set to the parameters including density, thickness and roughness of the membrane, the fitting results in the profile shown in FIG. 4, which converges to a solution shown in Table 3 as different from that shown in Table 2, and the R value of 0.015712 seems to be slightly improved in accuracy.
TABLE 3DensityThicknessRoughness(g/cm3)(nm)(nm)R valueSi2O3CH31.012398.300.440.015712Si substrate2.33—1.65
It is understood from the comparison between the results shown in Table 2 and the results shown in Table 3 that the magnitude relation of the interface roughness is reversed.
Such a case that plural solutions are present is often encountered, and it is difficult to evaluate as to which is the correct solution or as to whether both are ascribed to insufficient analysis only by using the measurement results shown in FIGS. 3 and 4. The phenomenon where the roughness values are reversed can be evaluated by measuring data to the higher angle region, but it is impossible to attain sufficient analysis in the case where the dynamic range is short.